Tullio Jappelli and Mario Padula April 2013 - CSEFWORKING PAPER NO. 330 Investment in Financial Literacy, Social Security and Portfolio Choice Tullio Jappelli and Mario Padula April

WWOORRKKIINNGG PPAAPPEERR NNOO.. 333300

Investment in Financial Literacy, Social

Security and Portfolio Choice

Tullio Jappelli and Mario Padula

April 2013

University of Naples Federico II

University of Salerno

Bocconi University, Milan

CSEF - Centre for Studies in Economics and Finance DEPARTMENT OF ECONOMICS – UNIVERSITY OF NAPLES

80126 NAPLES - ITALY Tel. and fax +39 081 675372 – e-mail: [email protected]

WWOORRKKIINNGG PPAAPPEERR NNOO.. 333300

Investment in Financial Literacy, Social

Security and Portfolio Choice

Tullio Jappelli* and Mario Padula**

Abstract We present an intertemporal portfolio choice model where individuals invest in financial literacy, save, allocate their wealth between a safe and a risky asset, and receive a pension when they retire. Financial literacy affects the excess return and the cost of stock market participation. Since literacy depreciates over time and has a cost related to current consumption, investors simultaneously choose how much to save, the portfolio allocation, and the optimal investment in literacy. This last depends on households' resources, its preference parameters and on how much financial literacy affects the returns on risky assets and the stock market participation cost, and the returns on social security wealth. The model implies one should observe a positive correlation between stock market par- ticipation (and risky asset share, conditional on participation) and financial literacy, and a negative correlation between the generosity of the social security system and financial literacy. The model also implies that the stock of financial literacy accumulated early in life is positively correlated with the individual's wealth and portfolio allocations later in life. Using microeconomic cross-country data, we find support for these predictions. JEL Classification: E2, D8, G1, J24 Keywords: Financial Literacy, Portfolio Choice, Saving. Acknowledgements: We thank the Observatoire de l'Eparagne Européenne (OEE) for financial support, and Didier Davidoff, and Christian Gollier for helpful suggestions. We also thank participants in the OEE Conference “Are Europeans lacking in financial literacy?", Paris, 8th of February, 2013, for comments. Any errors are our own.

* University of Naples Federico II, CSEF and CEPR. ** University “Ca’ Foscari” of Venice, CSEF and CEPR.

Table of contents

1. Introduction

2. Financial sophistication and portfolio performance

3. Theoretical background

3.1. Model I: Financial literacy and asset returns

3.2. Model II: Financial literacy and transaction costs

3.3. Empirical implications

4. Data

4.1. Financial literacy

4.2. Stockholding and risky asset share�

5. Empirical estimates

5.1. Financial literacy

5.2. Stockholding

5.3. Risky asset share

6. Conclusions

References

Appendix

6

1 Introduction

The classical theory of portfolio choice rests on the assumptions that there are no transaction

costs and that investors have full information about the risks and returns related to available

assets. If all investors face the same returns distribution and have the same information set,

differences in attitudes to risk affect the allocation of wealth between safe and risky assets,

but not the particular asset selected. Also, if the utility function exhibits constant relative

risk aversion, asset shares are independent of wealth. Under these assumptions, the rich man’s

portfolio is simply a scaled-up version of that of the poor man. However, recent empirical

studies show that household portfolios exhibit too much heterogeneity to be consistent with

the classical model. In particular, many individuals do not invest in stocks, a feature that has

come to be known as the stockholding puzzle (Haliassos and Bertaut, 1995).

The literature has tried to solve the puzzle by focusing on fixed entry costs. In the presence

of entry costs, investors benefit from stockholding only if the expected excess return from

participation exceeds the fixed cost. Since the gain increases with wealth, entry costs relate

wealth to stockholding. In particular, models with entry costs suggest that investors with wealth

below a certain threshold do not enter the stock market, and that only those whose wealth is

above this threshold do so. Empirical evidence documents a strong positive correlation between

stock market participation and financial wealth in many industrialized countries, providing

support to models featuring entry costs (Guiso et al., 2003; Vissing-Jorgensen, 2002). The

exact nature of entry costs, however, is not well understood. Are these monetary costs or

information costs? Do all investors face the same entry costs, or do they vary across investors?

Are there ways that allow investors to avoid or reduce entry costs?

In this paper we focus on lack of financial sophistication as a potential explanation for

limited financial market participation. In the paper we posit that, like other forms of human

capital, financial information can be accumulated, and that the decision to invest in financial

literacy has costs and benefits. Accordingly, we study the joint determination of financial

information, saving and portfolio decisions, theoretically and empirically. In the theoretical

model we posit that people are endowed with an initial stock of financial literacy, which they

acquire before entering the labor market, and that investing in financial literacy gives access

to better investment opportunities, raising the returns to risky assets or lowering entry costs.

Acquiring financial information however, entails costs in terms of time, effort and resources.

2

Our model delivers conditions for optimal saving, asset allocation and investment in financial

literacy. In particular, the model implies that financial literacy and stockholding are positively

correlated. However, the relation between the two variables is not a causal relationship, because

both variables depend on preference parameters, household resources, and the cost of acquiring

information. We find also that introducing a social security system (or making an existing

system more generous) reduces the incentive to save, to invest in financial literacy, and to

invest in risky assets, other things being equal. Therefore the social security system impacts on

stockholding in two ways: directly, by reducing discretionary wealth, and indirectly by reducing

the incentive to invest in financial literacy, thereby making stockholding less desirable.

In Section 2 we review the relevant literature, with a particular focus on studies of the

relation between financial sophistication and stockholding and work addressing the endogeneity

of financial literacy with respect to stockholding. Section 3 presents our theoretical model,

analyzing two distinct channels through which financial literacy affects asset allocation, i.e.

by raising assets returns (Model I), and by lowering transaction costs (Model II). To convey

the main insights in the simplest framework, we focus on a two-period model with an isoelastic

utility function. The model also features a social security system, showing that the replacement

rate (as an indicator of the generosity of the system) affects saving, portfolio choice, and

investment in financial literacy. The two models deliver several testable implications: (1) in

both models, the initial stock of financial literacy affects the trajectory of literacy later in

life; (2) Model I predicts that the stockholding decision does not depend on financial literacy,

while the share invested in risky assets increases with literacy; (3) Model II predicts a positive

relation between literacy and participation, but no relation between literacy and the share of

risky assets; (4) both models predict that social security affects portfolio choice, reducing stock

market participation and investment in risky assets; (5) the effect of social security on the

demand for risky assets depends on the initial stock of financial literacy.

In Section 4 we present our microeconomic data derived by merging the Survey of Health,

Ageing, Retirement in Europe (SHARE), which covers a representative sample of individuals

aged 50+ in Europe, and SHARELIFE, a retrospective survey of the same individuals. We

define indicators of financial literacy based on a series of questions available in SHARE (for

current literacy) and SHARELIFE (for literacy early in life). The SHARE indicator is framed

in the context of simple financial questions, and elicits the ability to understand and perform

3

simple financial operations. Mathematical competence does not necessarily span all domains

of financial literacy, for instance the awareness of specific financial products or tax incentives

to save. However, a minimal level of mathematical competence is needed to evaluate the

return and risk characteristics of financial products, as suggested by the limited impact of

financial education programs that do not explicitly address a minimal level of mathematical

literacy, (Carpena et al. 2011). Therefore, in the empirical section we will use indicators of

mathematical competence early in life available in SHARELIFE as a proxy for financial literacy.

Our regression results for the determinants of stockholding and of the share of risky assets are

presented in Section 5 . We find that the initial stock of financial literacy is strongly associated

with stockholding, but not with the share of risky assets, lending support to models in which

literacy lowers transaction costs (Model II). Section 6 summarizes our results.

2 Financial sophistication and portfolio performance

Many recent empirical studies using panel data on household portfolios find that low level of

financial sophistication is associated with poor risk diversification, inefficient portfolio alloca-

tions, and low wealth accumulation. Calvet et al. (2007) and (2009) find substantial hetero-

geneity in account performance using Swedish data, and that part of the variability of returns

across investors is explained by financial sophistication. In particular, they show that predic-

tors of financial sophistication (such as wealth, income, occupation, education) are associated

with higher Sharpe ratios, and that richer and more sophisticated households invest more effi-

ciently. Hackethal et al. (2012) use data on German brokerage accounts and find that years of

experience tends to contribute to higher returns. Feng and Seasholes (2005) find that investor

sophistication and trading experience eliminate reluctance to realize losses. 1 Campbell et

al. (2012) study investment strategies and the performance of individual investors in Indian

equities over the period 2002 to 2012.2 They study learning by relating account age (length

of time since the account was opened) and past portfolio mistakes to the performance of the

account, and find that account performance improves significantly with account age.

Other studies relate household portfolio decisions to direct indicators of financial literacy as

1See also Grinblatt and Keloharju (2001), Zhu (2002), and Lusardi and Mitchell (2007)2They find substantial heterogeneity in the time-series average returns, with the 10th percentile account

under-performing by 2.6 percent per month, and the 90th percentile account over-performing by 1.23 percentper month

4

a measure of sophistication. Van Rooij et al. (2011) rely on a special module in the Dutch

DNB Household Survey. The module includes questions on the ability to perform simple

calculations and to understand compound interest, inflation, and money illusion, and more

advanced questions on stock market functioning, characteristics of stocks, mutual funds, and

bonds, equity premiums, and the benefits of diversification. The authors find that financial

sophistication is associated with the probability to invest in the stock market and a higher

propensity to plan for retirement.

Guiso and Jappelli (2008) use data from the 2007 Unicredit Customer Survey (UCS) and find

that financial literacy is strongly correlated to the degree of portfolio diversification, even when

controlling for socioeconomic characteristics and risk aversion. Banks and Oldfield (2007) look

at numerical ability and other dimensions of cognitive function, in a sample of older adults in

the English Longitudinal Study of Ageing (ELSA) and find that numeracy levels are strongly

correlated with indicators of retirement savings and investment portfolios, understanding of

pension arrangements, and perceived financial security. Stango and Zinman (2009) analyze

the pervasive tendency to linearize exponential functions. Using the 1977 and 1983 Surveys

of Consumer Finances, they show that exponential growth bias can explain the tendency to

underestimate an interest rate given other loan terms, and the tendency to underestimate a

future value given other investment terms. Christelis et al. (2010) study the relation between

cognitive abilities and stockholding using SHARE data, and find that the propensity to invest

in stocks directly and indirectly (through mutual funds and retirement accounts) is strongly

associated with mathematical ability, verbal fluency, and recall skills.

One problem with these studies is that the incentive to invest in financial information de-

pends on household resources, because the benefit of stockholding (and therefore the cost of not

investing in the stock market) depends on the amount invested, see Delevande et al. (2008) and

Willis (2009). Furthermore, since the true stock of financial literacy is not observed by applied

researchers, empirical studies are affected by measurement error problems. The endogeneity

and measurement issues are similar to those arising in studies that estimate the returns to

schooling: any attempt to estimate the structural relation between schooling and wages must

deal with the endogeneity of the schooling decision and measurement errors in the quantity and

quality of education (Card, 2001). Some studies address these important econometric concerns

by using an instrumental variables approach, see Christiansen et al. (2008), Lusardi (2008), and

5

Behrman et al. (2012). In the next section we build on the insights in these paper and provide

a theoretical framework to study the relation between financial literacy and portfolio choice; in

successive sections we explore its empirical implications.

3 Theoretical background

We propose a model in which financial literacy, saving, and asset allocation are jointly deter-

mined. The model builds on the idea that investors can increase the payoff from their financial

portfolios by acquiring information on the rate of return, an idea first proposed by Arrow

(1987). We posit that people are endowed with an initial stock of financial literacy which is

acquired before they enter the labor market, and that investing in financial literacy gives access

to better investment opportunities, raising the expected return to saving (Model I) or reducing

the cost of participating in financial markets (Model II).3

In each period, people can invest their wealth in a safe asset, in a risky asset and in financial

literacy. Investment in literacy can directly raise the risk-free rate available to investors or the

mean of the return of the risky asset (e.g. through lower fees), reduce the variance of the return

of the risky asset through increased diversification, or affect the market entry cost for the risky

asset. Of course, there are several special cases, such as where the risk free rate is constant,

but the mean and variance of the risky asset are affected by financial literacy.

The stock of financial literacy depreciates over time, but people can acquire financial infor-

mation, which entails costs in terms of time, effort, or resources. Accordingly, agents choose

how much to invest in financial literacy, how much to save, and how much to invest in the risky

asset, given their initial level of literacy, the cost of literacy, the depreciation of the stock of

literacy, and their preferences. As noted by Arrow (1987), the incentive to invest in literacy

depends not only on the return to literacy (e.g. on the grounds that which raising literacy pro-

vides access to better investment opportunities and improved risk diversification) but also on

the amount of wealth available for financial investment (the incentive is an increasing function

of wealth).

Our theoretical analysis of Models I and II proceeds in two steps. In the first step, we

derive optimal saving, investment in risky assets, and investment in financial literacy in each of

the two models. In the second step we study how the generosity of the social security system

3We build on the no uncertainty single asset model proposed by Jappelli and Padula (2013).

6

- summarized in the replacement rate - affects these decisions. We find that in the presence

of mandatory contributions people have fewer resources to invest in the market (the familiar

Feldstein displacement effect), acquire less financial information, and have fewer incentives to

invest in stocks. The focus is to derive testable implications from the models in the simplest

framework.4

3.1 Model I: Financial literacy and asset returns

We assume that consumers live for two periods, and that they earn income y in period 0 and

retire in period 1. At the beginning of period 0 they have no assets but are endowed with a

stock of financial literacy, Φ0. The initial stock of literacy is what people know about finance

before entering the labor market. This therefore depends on schooling decisions and parental

background, neither of which we model explicitly.

Consumers can increase their stock of financial literacy by investing in financial literacy

in period 0. Literacy depreciates at the rate δ; the relative cost of literacy in terms of the

consumption good is p, which includes monetary and time costs incurred by consumers. The

stock of literacy therefore evolves according to:

Φ1 = (1− δ)Φ0 + φ (1)

where φ denotes investment in financial literacy.

The portfolio return is paid at the beginning of period 1 on wealth transferred from period

0 to 1. Denoting by ω the share of wealth invested in the risky asset, the gross portfolio return

is:

R(Φ1, α, ζ, ω) =

{θ1(Φ1, α, ζ, ω) with probability η(Φ1)θ2(Φ1, α, ζ, ω) with probability 1− η(Φ1)

where θ1(Φ1, α, ζ, ω) = Φα1 (1 + ωζ) and θ2(Φ1, α, ζ, ω) = Φ

α1 (1 − ωζ), α ∈ (0, 1), ζ > 0 and

η′(·) > 0 and η′′(·) < 0. If ω = 0, wealth is entirely invested in the riskless asset and the gross

return is Φα1 . If ω = 1, wealth is entirely invested in the riskless asset and the gross return

is Φα1 (1 + ζ) with probability η(Φ1) and Φα1 (1 − ζ) with probability 1 − η(Φ1). Therefore, the

4For ease of exposition, we analyze the two models separately. Of course it is possible to study a modelin which financial literacy affects the returns of risky assets (Model I) as well as participation costs (ModelII). The nested model has the same qualitative insights as Models I and II, although different quantitativeimplications. For instance, in the nested model the level of Φ0 that triggers stock market participation is lowercompared to Model II. Since we do not calibrate and simulate the theoretical models, but use them only toderive comparative static results, there is no real advantage in presenting the nested model.

7

mean return of the risky asset is {ζ[2η(Φ1)− 1] + 1}Φα1 and the first and second moment of the

equity premium distribution are [2η(Φ1) − 1]Φα1 ζ and Φ2α1 ζ, respectively. The Sharpe ratio is

thus an increasing function of financial literacy since η′(·) > 0, an assumption that is motivated

by the empirical literature on portfolio performance and financial sophistication surveyed in

Section 2.5

We assume that the utility function is isoelastic, so that consumers choose saving (s),

investment in financial literacy (φ) and the risky asset share (ω) to maximize:

(1− 1

σ

)−1 (c

1− 1σ

0 + βE0c1− 1

σ1

)

subject to c0 = y − pφ − s and c1 = R(Φ1, α, ζ, ω)s, where 0 < β < 1 is the discount factor

and E0(·) is the expected value of consumption in period 1. Appendix A.1 deals with the

logarithmic case. The first order conditions with respect to s, φ and ω are:

s1σ = βc

1σ0 E0R(Φ1, α, ζ, ω)

1− 1σ (2)

p

s− α

Φ1=

ση′(Φ1)[θ1(Φ1, α, ζ, ω)

1− 1σ − θ2(Φ1, α, ζ, ω)1−

1σ

](σ − 1)E0R(Φ1, α, ζ, ω)1−

1σ

(3)

θ1(Φ1, α, ζ, ω) =

[η(Φ1)

1− η(Φ1)

]σθ2(Φ1, α, ζ, ω) (4)

From (4), we obtain an expression for the share of wealth invested in the risky asset:

ω =η(Φ1)

σ − [1− η(Φ1)]σ

ζ {η(Φ1)σ + [1− η(Φ1)]σ}(5)

Equation (5) has an important implication for empirical work. In a cross-section of house-

holds reporting information on financial literacy (Φ1) and a risky asset share (ω), equation (5)

implies a positive association between the two variables. But clearly it cannot be concluded

from this correlation that a higher stock of literacy leads to a higher risky asset share, because

both variables are endogenous. In our model, equation (5) is therefore an equilibrium condition

between the optimal share and the optimal stock of literacy, not a reduced form equation. Thus

it implies that any factor that leads to higher financial literacy will also raise investment in the

risky asset.

5Notice that depending on the shape of η(Φ1) the equity premium can be negative if Φ0 is sufficiently low.This would make it optimal not to participate in the stock market even in the absence of transaction costs. Forinstance, if η(Φ1) is a normal cumulative distribution function with mean equal to µ, participating to the stockmarket is optimal only if Φ0 is large enough to make the optimal Φ1 > µ.

8

Using the budget constraint, (2) and (5), it can be shown that:

s =κ(Φ1, α, β, σ)

1 + κ(Φ1, α, β, σ)(y − pφ) (6)

where κ(Φ1, α, β, σ) = (2Φα1 )σ−1βσ {ησ(Φ1) + [1− η(Φ1)]σ}. Notice that κ(Φ1, α, β, σ) = β if

σ = 1.

From equations (3), (5) and (6) the optimal level of investment in literacy is implicitly

defined by:

p =κ(Φ1, α, β, σ)

1 + κ(Φ1, α, β, σ)

[α

Φ1+ λ(Φ1, σ)

](y − pφ) (7)

where:

λ(Φ1, σ) =ση′(Φ1)

σ − 1

{η(Φ1)

σ−1 − [1− η(Φ1)]σ−1

η(Φ1)σ + [1− η(Φ1)]σ}

The right-hand side of equation (7) is the marginal return from financial literacy investment.

The return has two components. The first component depends on αΦ1

; this component is positive

and captures the effect of literacy on the expected return to saving, and is also present in the

model without uncertainty (Jappelli and Padula, 2013). The second component depends on

λ(Φ1, σ), and is also positive, capturing the effect of literacy on the distribution of the risky

asset return. The first component is an increasing function of α; the second component is an

increasing function of η′(Φ1), i.e. of how much literacy raises the risky asset return.6

Straightforward application of the Dini theorem for implicit functions implies the following

proposition.

Proposition 1 If the right-hand side of (7) is a decreasing function of Φ1, the optimal levelof financial literacy is an increasing function of α (or β, Φ0, y) and a decreasing function of p(or δ), i.e.:

∂Φ∗1∂α

> 0,∂Φ∗1∂β

> 0,∂Φ∗1∂Φ0

> 0,∂Φ∗1∂y

> 0,∂Φ∗1∂p

< 0,∂Φ∗1∂δ

< 0

In addition, Appendix B shows that limσ→∞Φ∗1 > limσ→0 Φ

∗1 and provides sufficient condi-

tions for the marginal return from financial literacy to be a decreasing function of literacy.

Figure 1 plots the left-hand side (dashed line) and the right-hand side (continuous line) of

(7) as a function of Φ1. The continuous curve shifts up if α increases which implies that the

6Note that the marginal return of financial literacy increases with α, β, Φ0 and y and decreases with δ and p.In addition, if η(Φ1) = (1+e

−Φ1)−1, it can shown that: (a) λ(Φ1, σ) is a non-monotonic function of Φ1, increasingfor small values for Φ1 and decreasing for large values; (b) limΦ1→∞ λ(Φ1, σ) = 0; (c) λ(Φ1, σ) is a non-monotonicfunction of σ, increasing for small values of σ and decreasing for large values; (d) limσ→∞ λ(Φ1, σ) = 1− η(Φ1);(e) λ(Φ1, 0) = 0.

9

optimal level of financial literacy increases with α. An upward shift of the curve also obtains if

β, Φ0, y increase, while the line shifts down if p or δ falls.

One can solve equation (7) with respect to Φ1 and find the optimal value of financial literacy,

which in turn determines saving through (6) and the share of wealth invested in the risky assets

through (5). Given our interest in deriving testable implications for the portfolio choice, we

find it useful to focus on the share of wealth invested in the risky asset. From equation (5) it is

easy to verify that the share is positively associated with financial literacy, which leads to the

following proposition.

Proposition 2 If the right-hand side of (7) is a decreasing function of Φ1, the optimal shareof risky assets is an increasing function of α, β, Φ0, and y and a decreasing function of p andδ, i.e.:

∂ω∗

∂α> 0,

∂ω∗

∂β> 0,

∂ω∗

∂Φ0> 0,

∂ω∗

∂y> 0,

∂ω∗

∂p< 0,

∂ω∗

∂δ< 0

In addition, limσ→∞ ω∗ = 1

ζ> limσ→0 ω

∗ = 0

Proposition (2) has three implications. First, any factor leading to a high share of wealth

invested in risky assets also increases financial literacy. For instance, patient individuals (high

β) have relative high risky assets shares accompanied by relatively high levels of financial

literacy.7 For the same reason, any variable that affects literacy also affects the risky asset

share; for instance, as we shall see below, the generosity of the social security system affects

the risky asset share. Second, in the model the initial stock of literacy, Φ0, affects the risky

asset share only through its effect on the current stock of literacy Φ∗1. Therefore in a regression

framework Φ0 can be used as an instrument for Φ∗1. The third implication is that in standard

models with constant relative risk aversion (CRRA) the risky asset share does not depend on

wealth. Here we still have CRRA, but the share depends - through its effect on literacy - on

household resources. Therefore, the model delivers a positive correlation between the risky

asset share and wealth, contrary to the standard model.

3.1.1 Social security

We now introduce social security in the model and discuss its impact on financial literacy and

portfolio allocations. In period 0 consumers earn income y, net of social security contributions,

in period 1 they receive benefits equal to b.

7As noted above, this does not imply any causal link between financial literacy and risky asset share.

10

The first order conditions with respect to s, Φ1 and ω are:

s1σ = βc

1σ0 E0

R(Φ1, α, ζ, ω)[R(Φ1, α, ζ, ω) +

b

s

]− 1σ

(8)p

s− α

Φ1=

ση′(Φ1){[θ1(Φ1, α, ζ, ω) +

bsΦα1

]1− 1σ −

[θ2(Φ1, α, ζ, ω) +

bsΦα1

]1− 1σ

}(σ − 1)E0

{R(Φ1, α, ζ, ω)

[R(Φ1, α, ζ, ω) +

bs

]− 1σ

} (9)θ1(Φ1, α, ζ, ω) +

b

sΦα1=

[η(Φ1)

1− η(Φ1)

]σ [θ2(Φ1, α, ζ, ω) +

b

sΦα1

](10)

From (10), the share of wealth invested in the risky asset is:

ω =η(Φ1)

σ − [1− η(Φ1)]σ

ζ {η(Φ1)σ + [1− η(Φ1)]σ}

(1 +

b

sΦα1

)(11)

Using the budget constraint, (8) and (11) we can show that:

s =κ(Φ1, α, β, σ)

1 + κ(Φ1, α, β, σ)

[y − pφ− b

κ(Φ1, α, β, σ)Φα1

](12)

The optimal level of financial literacy is implicitly defined by:

p =κ(Φ1, α, β, σ)

1 + κ(Φ1, α, β, σ)

[α

Φ1+ λ(Φ1, σ)

] [y − pφ− b

κ(Φ1, α, β, σ)Φα1

]+ λ(Φ1, σ)

b

Φα1(13)

Equation (13) indicates that b has two effects (positive and negative) on the marginal return

to financial literacy. The negative effect causes the optimal level of financial literacy to decrease

if b increases. The effect is also present in the model without uncertainty on asset returns (see

Jappelli and Padula, 2013) and is due to the offsetting of social security with private wealth.

If b increases, social security wealth increases, and therefore s and Φ1 decrease. The positive

effect is new to the model with uncertain asset returns, and is due to b being not uncertain.

The higher is b, the more individuals invest in the risky asset, which induces these individuals

to invest more in financial literacy. If α is large enough, the former effect prevails, and the

optimal level of financial literacy is a decreasing function of b. 8 This results is summarized in

the following.

Proposition 3 If the right-hand side of (13) is a decreasing function of Φ1, for large enoughα the optimal level of financial literacy is a decreasing function of b, i.e.:

∂Φ∗1∂b

< 0

8The condition is α > Φ1κ(Φ1, α, β, σ)λ(Φ1, σ) and therefore the value of α that makes the optimal Φ1 to bea decreasing function of b depends on the values of the remaining model parameters. For instance, the conditionis satisfied if β = 0.99, δ = 0.3, Φ0 = 1, σ = 0.5, y = 0.9, p = 0.1, and α > 0.23. More generally, the higher isσ, the higher will be the value of α, which makes the optimal Φ1 a decreasing function of b.

11

Equation (13) implies that Φ0 also affects the link between b and financial literacy. Depend-

ing on the model’s parameters, a higher Φ0 can attenuate the effect of b on Φ1. Defining the

right-hand side of (13) as Ξ (α, β, δ,Φ0,Φ1, σ, y, p, b), we can immediately verify the following

proposition.

Proposition 4 A higher Φ0 attenuates the effect of b on the optimal level of financial literacyif:

∂Ξ (α, β, δ,Φ0,Φ1, σ, y, p, b)

∂Φ1∂b< 0

Proposition 4 implies that the sign of∂Φ∗1∂Φ0∂b

is the same as the sign of ∂Ξ(α,β,δ,Φ0,Φ1,σ,y,p,b)∂Φ1∂b

.

Figure 2 shows that the optimal level of financial literacy is a decreasing function of b. There

are two lines in the figure, for low and high values of Φ0, showing that a higher Φ0 attenuates

the effect of the generosity of the social security systems on financial literacy, an implication of

the model that we will confront with empirical evidence.

3.2 Model II: Financial literacy and transaction costs

We now assume that acquiring financial literacy reduces the transaction cost of entering the

stock market, rather than assuming that it raises the asset return (as in Model I). In particular,

we assume that:

R =

1 + ωζ with probability η1− ωζ with probability 1− ηwhere η > 1

2. Moreover, we assume that if ω > 0, the consumer incurs a transaction cost equal

toΦ−γ1γ

, with γ > 0.

Under these assumptions the intertemporal budget constraint is

c0 +c1R− pΦ1 + p(1− δ)Φ0 −

Φ−γ1γ

1l {ω > 0} = y

where, as before, c0 and c1 denote consumption in period 0 and 1, Φ0 and Φ1 the stock of

financial literacy in period 0 and 1, δ the depreciation rate of the stock of literacy, p and y the

price of financial literacy investment and first-period income and 1l {·} is an indicator function.

As in Model I, φ = Φ1 − (1− δ)Φ0.

12

Again, we assume that the utility function is isoelastic. To compute the indirect utility

from investing in the risky asset, let us assume also that ω > 0. The first order conditions with

respect to s, φ and ω are:

s1σ = βc

1σ0 E0R

1−1σ

p = Φ−(1+γ)1

1 + ωζ =

(η

1− η

)σ(1− ωζ)

which reduce to the logarithmic case if σ = 1 (see Appendix A.2). The first order condition with

respect to s delivers the standard Euler equation for consumption. The first order condition

with respect to φ implies that:

Φ1 =

(1

p

) 11+γ

(14)

Notice that equation (14) is not a reduced form, because it is obtained assuming ω > 0, a

condition that holds only if the utility from investing in the risky asset is greater than that from

not investing. From the first order condition with respect to ω, the share of wealth invested in

the risky asset is:

ω =ησ − (1− η)σ

ζ[ησ + (1− η)σ](15)

Equation (15) implies that the conditional risky assets share does not depend on financial

literacy. Using the Euler equation for consumption, (14), (15) and the budget constraint, we

obtain:

cI0 =ỹ

1 + β̃(16)

and:

cI1 = (2β)σ cI0 ×

ησ with probability η

(1− η)σ with probability 1− η(17)

where β̃ ≡ 2σ−1βσ [ησ + (1− η)σ] and ỹ ≡ y − pγ

1+γ

(1 + 1

γ

)+ pΦ0(1− δ).

The indirect utility of investing in the risky asset (V I) is computed using (16) and (17) and

can be written as:

V I =(

1− 1σ

)−1 [(1 + β̃

) 1σ ỹ1−

1σ − (1 + β)

]If the consumer does not invest in the risky asset, cNI0 =

y1+βσ

and cNI1 = βσcNI0 . Therefore,

the indirect utility of not investing in the risky asset is:

V NI =(

1− 1σ

)−1 [(1 + βσ)

1σ y1−

1σ − (1 + β)

](18)

13

The utility gain from stockholding is a monotonically increasing function of Φ0 since the

utility of investing in the risky asset is an increasing function of Φ0, while the utility of not

investing in risky assets is not affected. Therefore, we can immediately verify the following

proposition:

Proposition 5 The utility gain from investing in the risky asset, V I − V NI , is an increasingfunction of Φ0.

Proposition 5 implies that (in a random utility setting) the probability of stock market

participation increases with Φ0, an important difference between Model II and Model I. From

proposition 5 it can be shown further that the optimal level of financial literacy is an increasing

function of Φ0. The argument proceeds as follows. Note that if Φ0 = 0, the utility of investing

in the risky asset is negative, i.e. V I < V NI when the following condition holds:

p >

[γ

1 + γy(1− Ψ̃

)] 1+γγ. (19)

where Ψ̃ ≡(

1+βσ

1+β̃

) 1σ−1

. 9 Condition (19) implies that if the price of financial literacy

is sufficiently large, it is not optimal to invest in the risky asset if Φ0 = 0. Moreover,

limΦ0→+∞ VI − V NI = +∞, which, together with condition (19), implies that one can find

a value for Φ0, say Φ0, such that ω > 0 if Φ0 > Φ0. Since it is optimal to invest in financial

literacy only if ω > 0, this implies that Φ0 has to be high enough to trigger investment in

financial literacy. The argument is summarized in the following proposition.

Proposition 6 If condition (19) is satisfied, there exists a value for Φ0, Φ0, such that VI =

V NI , i.e.:

Φ0 =1

p(1− δ)

[(1 + γ

γΨ̃

)p

γ1+γ +

y

Ψ̃

(Ψ̃− 1

)]

Moreover, if Φ0 ≥ Φ0, then ω > 0 and φ∗ > 0.

The empirical implication of proposition 6 is that if the initial level of financial literacy

differs across individuals, Φ1 and Φ0 are positively correlated.

9Notice that if γ becomes zero, the right-hand-side of (19) also goes to zero, which implies that it is notoptimal to invest in the risky asset market if p > 0.

14

3.2.1 Social security

As in Section 3.1.1, we assume that income net of social security contributions is earned in

period 0 and social security benefits b are paid in period 1. The budget constraint is:

c0 +c1R− pΦ1 + p(1− δ)Φ0 −

Φ−γ1γ

1l {ω > 0} = y + bR

and the first order conditions with respect to s, φ and ω are unaffected.

The indirect utility of investing in the risky asset is:

V I =(

1− 1σ

)−1 (1 + β̃) 1σ (ỹ − t+ bR

)1− 1σ

− (1 + β)

and that of not investing:

V NI =(

1− 1σ

)−1 (1 + βσ) 1σ (y + bR

)1− 1σ

− (1 + β)

By comparing V I and V NI we can show that the analog of condition (19) is:

p >

[γ

1 + γ

(y +

b

R

)(1− Ψ̃

)] 1+γγ. (20)

If condition (20) holds, we can show that for Φ0 equal to zero, VNI > V I , leading to the

following proposition.

Proposition 7 If condition (20) is satisfied, there exists a value for Φ0, Φ0, such that VI =

V NI , i.e.:

Φ0 =1

p(1− δ)

[(1 + γ

γΨ̃

)p

γ1+γ +

(y + b

R

Ψ̃

)(Ψ̃− 1

)]

Moreover, if Φ0 ≥ Φ0, then ω > 0 and φ∗ > 0.

There are two implications of proposition 7. First, if p is large enough, the utility gain from

investing in the risky assets becomes positive for sufficiently high values of Φ0, as in proposition

6. Second, Φ0 is an increasing function of b. This implies that the higher is b, the higher is

the initial level of financial literacy that triggers stock-market participation and investment in

financial literacy.

To appreciate the effect of the generosity of the social security system on stockholding, note

that both V I and V NI are increasing functions of b. From proposition 6, if Φ0 > Φ0 and b = 0,

V I > V NI . Furthermore, as b increases, V I approaches V NI from below. If σ ≥ 1, V I and V NI

diverge, but V I does so at a slower rate than V NI . If σ < 1, limb→∞ VI − V NI = 0−. This

leads to the following proposition.

15

Proposition 8 There is a value for b, say b, such that V I = V NI . Moreover, if b ≥ b, thenω = 0 and φ∗ = 0.

Proposition 8 implies that the generosity of the social security system is negatively correlated

with stock market participation and investment in financial literacy.

3.3 Empirical implications

Section 3 shows two channels through which financial literacy can affect portfolio choice. Model

I focuses on the effect of literacy on the distribution of asset returns, and posits that higher

(and safer) returns are associated with higher financial literacy. By assuming that higher

financial literacy reduces the cost of stock market participation, Model II also implies a positive

link between financial literacy and portfolio returns. Both models predict a positive effect of

literacy earlier in life (Φ0) on the trajectory of financial literacy (Φ1), but differ along important

dimensions. Model I implies that in an heterogeneous population, where people are identical

except for their initial stock of literacy, (a) everyone participates in the stock market, and (b) the

risky asset share is positively related to financial literacy. Model II implies that (a) participation

depends on literacy, but (b) the asset share, conditional on participation, does not. Therefore,

to compare the validity of the two models we need to study the correlation between asset shares,

participation, and financial literacy. A positive correlation between literacy and asset shares,

and no correlation between literacy and participation, would support Model I. Alternatively, a

positive correlation between literacy and stockholding and no correlation between literacy and

the risky asset share would support Model II.

In our empirical study we verify some other important implications of the model. In par-

ticular, we focus on the role of social security in the incentives to accumulate financial literacy,

exploiting cross-country variation in the replacement rate. In particular, we test propositions

3 and 4 for Model I and 7 and 8 for Model II including in our regressions the replacement rate

and its interaction with Φ0.

To make our tests operational, we estimate the linear projections of financial literacy, asset

shares, and stock market participation on the initial level of literacy and the social security

replacement rate; the projections can be seen as linear approximations of the model’s reduced

form equations. To account for the role of other potential effects on stockholding and on the

risky asset share, we control for a number of other variables, which are held constant in the

16

theoretical model. Denoting households by i, countries by c, and survey years by t, leads to

the following specification:

yi,c,t = dc + ξ1Φi,0 + ξ2Φi,0 × ρc + ξ3xi,t + εi,t (21)

where dc is a country dummy, ρc is the country-level replacement rate, xi,t is the vector of

additional variables affecting portfolio choice, εi,t an error term and yi,c,t is either the current

stock of financial literacy (Φi,t), stock market participation or share of wealth invested in risky

assets (ωi,t). Suppose first that yi,c,t is financial literacy. Propositions 1 of Model I and 5

of Model II imply a positive correlation between Φi,tand Φi,0, i.e. ξ1 > 0. Furthermore, both

Model I and II indicate that a higher replacement rate reduces the effect of Φi,0 on Φi,t, implying

ξ2 < 0, see proposition 4 of Model I and proposition 7 of Model II.

If yi,c,t denotes the share of risky assets, in Model I ξ1 > 0 and ξ2 < 0, since the share of risky

assets is an increasing function of financial literacy, while in Model II ξ1 = ξ2 = 0, because it is

conditional on stock market participation, the share of wealth invested in the risky asset does

not depend on financial literacy. When yi,c,t is the indirect utility of stockholding, the reverse

implications apply to stock market participation. Model I predicts that everyone should invest

in stocks ( ξ1 = 0 if the equity premium is positive). In Model II the utility of participating

is an increasing function of Φ0 (ξ1 > 0) while b attenuates the effect of Φ0 on the stockholding

decision (ξ2 < 0), see propositions 7 and 8, respectively.

The list of x variables is potentially large, but three variables are prominent in our exercise.

First, the incentive to accumulate wealth and to invest in financial literacy depends on age,

because younger individuals hold less wealth and therefore have a lower incentive to invest in

financial literacy, see Jappelli and Padula (2013). A second important element is that financial

literacy is likely to be correlated with education attainment. Third, households’ resources

(real estate, financial wealth and household disposable income) affect the incentives to acquire

financial literacy, and also stock market participation and – possibly – asset shares. As we

explain in the next section, to estimate the model we use cross-country microeconomic data

with information on portfolio composition, current financial literacy and financial literacy early

in the life-cycle.

17

4 Data

We test the theoretical predictions of Models I and II using data from SHARE, a representative

sample of those aged 50+ in 11 European countries. This dataset has several advantages.

First, SHARE provides good proxies for financial sophistication, based on responses to specific

questions that allow us to construct an indicator of financial literacy. Second, the survey

provides data on mathematical and language skills before entry to the labor market (at school

age), providing a valuable instrument to allow joint determination of literacy, stockholding and

the asset share. Third, SHARE provides consistent and comparable information on household

portfolios (transaction accounts, bonds, stocks, mutual funds, and retirement accounts) allowing

us to measure direct stockholding, indirect stockholding through mutual funds, and respective

asset shares. Finally, the cross-country dimension of SHARE allows us to study portfolio

decisions and their interactions with financial literacy, in countries with relatively generous

public pension systems (e.g. France and Italy) and to contrast them with data from countries

where occupational pension schemes (e.g. Netherlands) play a prominent role.

SHARE data refer to 2003 and 2006 and cover many aspects of the well-being of elderly

populations, ranging from socio-economic to physical and mental health conditions. 10 Wave 1

refers to 2003 and covers 11 European countries (Austria, Belgium, Denmark, France, Greece,

Germany, Italy, Netherlands, Spain, Sweden, Switzerland). Wave 2 refers to 2006 and includes

these 11 countries plus the Czech Republic, Poland, and Ireland. 11 Wave 3 (which excludes

Ireland) is known as SHARELIFE, and records individual life-histories for Wave 1 and 2 re-

spondents, based on the so-called life-history calendar method of questioning, which is designed

to help respondents recall past events more accurately. The sample includes 14,631 observa-

tions obtained merging Wave 1 and SHARELIFE, and 18,332 observations merging Wave 2

and SHARELIFE. Selected sample statistics are reported in Table 1, separately for Waves 1

10We use data from SHARELIFE release 1, dated November 24th 2010 and SHARE release 2.3.1, dated July29th 2010. SHARE data collection is funded primarily by the European Commission through the 5th FrameworkProgramme (Project QLK6-CT-2001- 00360 in the thematic “Quality of Life”), the 6th Framework Programme(Projects SHARE-I3, RII-CT- 2006-062193, COMPARE, CIT5-CT-2005-028857, and SHARELIFE, CIT4-CT-2006-028812) and the 7th Framework Programme (SHARE-PREP, 211909 and SHARE-LEAP, 227822), with ad-ditional funding from the U.S. National Institute on Aging (U01 AG09740-13S2, P01 AG005842, P01 AG08291,P30 AG12815, Y1-AG-4553-01 and OGHA 04-064, IAG BSR06-11, R21 AG025169), and various national sources(see www.share-project.org/t3/share/index.php for a full list of funding institutions). For information on sam-pling and data collection see Klevmarken (2005).

11In Wave 2, a refresher sample is drawn for all countries except Austria and the Flemish part of Belgium.The refresher sample includes only one age-eligible (50+) person per household.

18

and 2. The variables have the same definitions in 2003 and 2006, except for income which is

gross of taxes in 2003 and net of taxes in 2006. Therefore, we report separate estimates for the

two samples.

In both wages, the average age of the household head is 64 years, the fraction of females

is just above 50 percent, and singles account for 24 percent of the sample. The fraction of

high-school and college graduates is also stable in the two waves, with high school graduates

accounting for 30 percent of the sample, and college graduates for another 20 percent. These

figures hide considerable cross-country heterogeneity. Nordic countries feature a much higher

share of college graduates than Italy, Spain and Greece. The fraction of couples ranges from 53

percent in Austria to 67 percent in Belgium. Household financial wealth also varies consider-

ably, with Switzerland clearly the leader, followed by Sweden, while households in Italy, Spain

and Greece report much lower gross financial assets. The ranking between Scandinavian and

Mediterranean countries is reversed for real assets, with median values of around 157,000 euro

in Belgium, 139,000 euro in Italy and 65,000 euro in Sweden.

4.1 Financial literacy

The questionnaire for Waves 1 and 2 of SHARE includes four questions referring to simple

financial decisions, on which basis we construct a measure of financial literacy. The first question

is aimed at understanding whether respondents know how to compute a percentage. The second

and third questions ask respondents to compute the price of a good offered at a 50 percent

discount, and the price of a second-hand car that sells at two-thirds of its cost when new. The

fourth question is about understanding interest rate compounding in a saving account, and

is commonly considered a good proxy for financial literacy, see Lusardi and Mitchell (2008),

Lusardi et al. (2010) and Hastings et al. (2012).12

The first three questions reflect the ability to apply minimal amount of mathematical lit-

eracy, and the fourth is a typical question in virtually all financial literacy assessment studies.

Following Dewey and Prince (2005) we combine the answers to the four questions into a sum-

mary indicator as a measure of the current stock of literacy Φit. Details on the wording of the

questions and the construction of the indicator are given in Appendix C and discussed further

in Christelis et al. (2010).

12The interest rate question is one of three financial literacy questions in the Health and Retirement Study(HRS) and is used in several other international surveys.

19

Our approach recognizes that a certain level of mathematical competence is a necessary

condition for financial literacy; in fact, any financial literacy assessments invariably includes

questions that require some amount of mathematical literacy. For instance, a minimum level of

competence in mathematical literacy is required to compute a percentage, to understand the

meaning of interest compounding, or to use the concept of uncertainty, and to evaluate asset

returns. Therefore, in our empirical application we are confident that our SHARE indicator of

financial literacy is closely correlated with a broader concept of financial literacy, such as that

provided by the OECD, which defines financial literacy as: “Knowledge and understanding of

financial concepts, and the skills, motivation and confidence to apply such knowledge and un-

derstanding in order to make effective decisions across a range of financial contexts, to improve

the financial well-being of individuals and society, and to enable participation in economic life.”

In the model in Section 3 Φi0 is the financial literacy endowment before entering the la-

bor market. SHARE retrospective data (SHARELIFE) provide a plausible measure of this

endowment. Survey participants report their mathematical ability at age 10 in response to

the question: ”How did you perform in Maths compared to other children in your class? Did

you perform much better, better, about the same, worse or much worse than the average?”

13 While mathematical does not span exactly the same domain of financial literacy, ongoing

research shows that there is a close correlation between the two concepts of literacy. Indeed,

preliminary results from the most recent PISA survey show that financial literacy among the

young is strongly correlated with mathematical literacy, and that financially sophisticated re-

spondents are also likely to be relatively skilled in terms of mathematical competence. 14

The indicator of current financial literacy (Φit) ranges from 1 to 5, with a sample mean

of 3.43 for Wave 1 and 3.48 for Wave 2 - see Table 1. In both years the indicator exhibits

considerable sample variability, with a coefficient of variation of 0.32. Our measure of initial

literacy (Φi0) also ranges from 1 to 5, with similar means and coefficients of variation. The

correlation between Φit and Φi0 is 0.28. Our measures of Φit and Φi0 are imperfect proxies

of financial literacy, and can therefore be seen as error- ridden measures of financial literacy.

To the extent that measurement error is non-differential, the measured correlation actually

underestimate the true correlation.

13The survey also asked about relative performance in language, and we use this variable in our robustnesschecks.

14The relation between mathematical and financial literacy is discussed at length in (2013).

20

4.2 Stockholding and risky asset share

SHARE provides detailed information on both financial and real assets. Financial assets include

bank and other transaction accounts, government and corporate bonds, stocks, mutual funds,

individual retirement accounts, contractual savings for housing, and life insurance policies. The

questions on real assets refer to the value of the house of residence, other real estate, business

wealth and vehicles (see Christelis et al., 2010).

We adopt two definitions of stockholding: direct stockholding and total stockholding, de-

fined as stocks held directly plus stocks held through mutual funds and investment accounts

(assuming that whoever holds mutual funds and retirement accounts has some stocks in them).

Figure 3 reports participation in direct and total stockholding in the 11 countries in our sample.

The prevalence of direct stockholding ranges from less than 6 percent in Greece and Italy to 49

percent in Sweden. Total stockholding goes from about 10 percent in Austria, Spain and Italy

to 75 percent in Sweden. Broadly speaking, stockholding increases from Southern to North-

ern Europe, with a group of intermediate countries (France, Germany, Belgium, Netherlands

and Switzerland). Sweden and Denmark have by far the highest direct and total stockholdings,

while Austria, Spain, Greece and Italy are at the other end of the spectrum. The graph suggests

that country effects are potentially quite important for explaining the stockholding decisions

of European investors. Our regression framework therefore introduces country fixed effects in

each of the specifications.

In contrast, Figure 4 shows that cross-country differences in conditional asset shares (ex-

cluding households with zero stockholding) are much less pronounced. The share of wealth

held directly in stocks ranges from 20 percent in Denmark and Sweden to 35 percent in Austria

and Italy. Therefore, the relatively small number of stockholders in Italy and Greece invest

in stocks more than the average European household. Northern countries feature intermediate

values for the share of risky assets, with the notable exception of Sweden where risky assets

represent almost 40 percent of financial wealth.

21

5 Empirical estimates

5.1 Financial literacy

Table 2 presents the OLS regressions for financial literacy, separately for Waves 1 and 2. Each

regression also includes a full set of country dummies; for brevity these coefficients are not

reported here.15 In the baseline specification in column 1 we find that Φi0 is a strong predictor

of Φit. The coefficient of Φi0 is large (0.30) and quite precisely estimated (the standard error

is 0.025). This finding is consistent not only with our model’s prediction but also with other

evidence on the long-term impact of early-life conditions (see, for instance, Herd et al., 2012).

The age coefficient is negative (-0.017), and shows that in this sample of aged individuals, the

stock of literacy falls by about 0.5 percent per year, suggesting that households incentives to

invest in financial literacy decline with age, when wealth also tends to fall.

The coefficient of the female dummy is also negative. That women have lower financial

literacy than men which is in line with the results from other studies (see Lusardi and Mitchell,

2008). Our model also predicts a negative effect because women generally have less wealth

than men and therefore fewer incentives to invest in financial literacy. Education is strongly

correlated with literacy (a coefficient of 0.40 for high-school and 0.59 for college graduates).

The positive correlation is also consistent with our model, because higher human capital and

lifetime income are associated with a higher stock of financial literacy. The negative signs of

the coefficient of the dummy for singles and family size is likely to depend on the fact that

these variables are negatively correlated with wealth. The coefficient of the interaction term

between the replacement rate and Φi0 is negative, indicating that more generous social security

systems attenuate the effect of Φi0 on later financial literacy, as predicted by Models I and II.16

The regression implies that a 1 percent increase in the replacement rate reduces the effect

of Φi0 on Φit by about 0.16 percent. Figure 6 shows how the effect of Φi0 on Φit varies across

countries, depending on the replacement rate. The effect is relatively large for countries such

as the Netherlands (a 1 standard deviation increase in Φ0 leads to an increase in Φit of 0.23)

and Switzerland (0.22), and is relatively small for Italy (0.17) and Spain (0.14), which have

relatively high replacement rates.

15Country dummies provide a partial but important control for the cost of financial literacy. But the costof financial literacy can also vary between households within the same country. Therefore, we assume that theresidual household level variation in the cost of literacy is orthogonal to our chosen set of controls.

16The replacement rate is drawn from Disney (2004).

22

In column 2 of Table 2 we add health status and log disposable income to rule out that

the effect of Φi0 on Φit is simply due to the correlation between Φi0 and these variables. The

coefficients of health status and log income are positive and statistically different from zero,

while the other coefficients (and of Φi0 in particular) are not affected. In the next regression

(column 3) we check the stability of the coefficients replacing the age variable with a full set

of age dummies. The pattern of the estimated coefficients of the age dummies (not reported

for brevity) indicates that the stock of financial literacy falls during retirement, while the

coefficients of the other variables are unaffected. Of course, in cross-sectional data we cannot

distinguish between age and cohort effects, and therefore an interpretation of the age dummies

in terms of cohort effects (literacy improves for younger generations) would be equally possible.

The other three regressions in Table 2 repeat the estimation using data from Wave 2. The size

and significance of the coefficients is very similar to Wave 1. In particular, the coefficient of Φi0

ranges between 0.27 to 0.29 and is precisely estimated, while that of the interaction between

Φi0 and ρc is negative, confirming the model’s prediction that a more generous social security

system attenuates the effect of Φi0.17

5.2 Stockholding

Next, in order to distinguish between our two alternative models of how financial literacy affects

portfolio choice (through the returns or the transaction cost channel), we investigate the deter-

minants of the decision to invest in stocks (or other risky assets). In order to distinguish the

determinants of financial market participation, we study separately direct and total stockhold-

ing, which also includes stocks owned through managed investment accounts and mutual funds.

We use the same specification as for financial literacy, relating stock market participation to

demographic variables, education, indicators of household resources, and most important for

the present study, the initial stock of literacy Φi0.

The results for direct and total stockholding are reported in Tables 3 and 4, respectively.

In each of the tables columns 1 to 3 refer to Wave 1, and columns 4 to 6 to Wave 2. The

results show that both direct and total stockholding fall with age, a result found in several

other studies (see, for instance, Ameriks and Zeldes, 2004). The results are similar for direct

17Φ0 is not the only early childhood variables that can affect later financial literacy. In a related paper,Jappelli and Padula (2013) add to the financial literacy regression a number of other controls for early liferesources in the house, family cultural background and health conditions. These augmented regressions confirma positive and sizable effect of Φ0 on later financial literacy.

23

and total stockholding and for the two waves of SHARE, and imply that one year is associated

with a reduction in stockholding of between 0.1 and 0.2 percent.18

Introducing age as a linear variable does not affect any of our results, as shown in Tables 3

and 4 columns 3 and 6 where a set of age dummies replaces the linear age term. The coefficient

of the female dummy is negative but imprecisely estimated, possibly because financial literacy

captures part of the gender gap in stockholding, as argued in a recent paper by Alemberg and

Dreber (2011).

Singles are 10 percent less likely to invest in stocks than couples (the omitted category). But,

being single is correlated with household resources. In fact, controlling for income and wealth

reduces the effect by a factor of roughly 3. High-school and college graduates are, respectively

4.6 and 15 percent more likely than high school drop-outs to hold stocks directly. The coefficient

of initial literacy (Φi0) is positive and statistically different from zero. Columns 1 and 4 in

Table 3 show that an increase of one standard deviation in Φi0 is associated with an increase in

stockholding of 7 percentage points, and the result is quite stable across specifications. Results

for total stockholding (Table 4) are similar, with a slightly smaller effect on Φi0 (about 5.5

points). These results are consistent with the prediction of Model II, that financial literacy

triggers participation by reducing entry costs.

Finally, we interact Φi0 with the replacement rate (ρc) to check whether the generosity of

the social security system affects the incentive to acquire financial information. Note that the

replacement rate varies only across countries and therefore the direct effect of ρc is absorbed by

the country dummies, which are included in all regressions. The coefficient of the interaction

term is negative (ξ2 < 0), meaning that a higher replacement rate attenuates the effect of Φi0

on stockholding, consistent again with Model II. The effect is similar across specifications and

definitions of stockholding (direct or total), meaning that a 1 percent increase in the replacement

rate reduces the effect of Φi0 on stock-ownership by about 0.06 percentage points.

Figure 5 shows how the effect of Φi0 on direct stockownership varies with the replacement

rate. The effect is a decreasing function of the replacement rate, i.e., countries with relatively

low replacement rates show stronger effects. For instance, in the Netherlands and in Switzerland

a one standard deviation increase in Φi0 increases participation by 4 percentage points, while

in Italy the increase is only 1.6 points.

18Note again that in our context we cannot distinguish between a genuine age effect and a cohort effect whereyounger cohorts are more likely to invest in stocks.

24

5.3 Risky asset share

The final set of results are for the regressions for asset share invested in stocks. In this case

again we use two definitions of stockholding (direct and total). Model I shows that financial

literacy might affect not only stock market participation but also the share of risky assets,

allowing people to invest in assets with higher returns. As a result, people with higher financial

literacy might also invest more in risky assets. We estimate a Tobit model for the financial

asset share invested in stocks and find no effect of financial literacy on the risky asset share (at

conventional significance levels), regardless of how share is defined (direct stockholding as in

Table 5, or total stockholding as in Table 6). In conjunction with the evidence on stock market

participation, the results lend support to models (such as Model II) where literacy affects the

decision to own stocks but not the asset share invested.

Note that, compared to stock market participation, asset shares are more volatile and more

difficult to predict. Most of the estimated coefficients, while reasonably signed, are not precisely

estimated, with the notable exception of the high-school and college dummies, which suggests

a positive relation between education and the share of risky assets.

According to standard portfolio theory, the main determinant of the share of risky assets is

the coefficient of relative risk aversion (the lower the risk aversion, the higher the share). In the

special case of CRRA the share is independent of wealth. Our results reveal a positive relation

between household resources and asset shares, suggesting that exposure to stock market risk

tends to be higher for the wealthy. The dummy for singles has a negative and statistically

significant coefficient, which is somewhat reduced if we control for household resources (income

and wealth). Better health status is also positively associated with a higher share of risky

assets, consistent with the argument that people exposed to background risks (such as health)

tend to limit exposure to risks that can be avoided.

The regressions in Tables 5 and 6 indicate also that the effect of Φi0 is positive, but

rather small and not precisely estimated. We therefore use Φi0 as the identifying variable

in a selectivity-model of the asset share, assuming that Φi0 affects the participation decision

but not the asset share. The main advantage of a selectivity model is that we can focus on

the conditional asset share, i.e. restrict attention to the sample of actual stockholders. The

model also allows us to distinguish between the extensive and intensive margins (respectively

the decision Mills ratio to invest in stocks and the amount invested). The respective results for

25

direct and indirect stockholding are reported in Tables 7 and 8.

The selectivity model confirms many of the results of the Tobit regressions, in particular

that household resources affect conditional asset shares not just the participation decision. The

age effect is positive and statistically different from zero. Aging by 1 year is associated with a

0.3-0.5 percentage points increase in the share of wealth invested in directly held stocks (0.6%

for total stockholding). However, the pattern of the age dummies coefficients, not reported here,

rejects the hypothesis of a linear age effect in favor of a hump-shaped profile. The coefficients of

the other variables are less precisely estimated than in the Tobit model. The selectivity model

is also consistent with non-random selection since, in most specifications, the coefficient of the

inverse Mills ratio is statistically different from zero for both direct and total stockholding.

6 Conclusions

Identifying the channels through which financial literacy affects household saving behavior is a

challenge for empirical research. Previous findings of a positive correlation between measures of

financial literacy and portfolio outcomes do not necessarily mean that financial literacy improves

portfolio diversification, or that it causes higher stockholding and higher saving. Therefore

previous evidence is not sufficient grounds for policies aimed at raising levels of financial literacy

among the general population, or some target groups. To understand the causal nexus between

financial literacy and portfolio choice it is necessary to identify the explicit channel through

which literacy affects portfolio decisions, and to explicitly address the endogeneity of literacy

with respect to portfolio choice. In this paper we focused on lack of financial sophistication as a

potential explanation for limited financial market participation. We posit that, like other forms

of human capital, financial information can be accumulated, and that the decision to invest

in financial literacy has costs and benefits. Accordingly, we studied the joint determination

of financial information, saving, and portfolio decisions, both theoretically and empirically.

We assumed that financial literacy is costly to acquire but allows individuals to access better

financial investment opportunities. In particular, we proposed two channels through which

financial literacy might affect saving behavior, by raising the returns on risky assets and by

reducing the transaction costs to enter the stock market.

We tested some of the implications of the model using household data drawn from the

Survey of Health, Ageing, Retirement in Europe (SHARE). We found that the link between fi-

26

nancial literacy and portfolio choice is likely due to the fact that financial sophistication reduces

participation costs. The empirical results show also that the level of financial sophistication

before individuals enter the labor market affects financial literacy throughout life. Therefore

policies aimed at improving the level of financial education early in the life-cycle are likely to

have long-run consequences on portfolio allocations.

We also exploited the cross-country dimension of our data to test an important implication

of our model, namely the role of social security in shaping the decision to accumulate financial

literacy. The results indicate that more generous social security systems reduce the incentives

to accumulate wealth and invest in stocks, attenuating the effect of initial literacy on the

stockholding decision, which is consistent with the model’s prediction.

27

References

Almenberg, Johan, and Anna Dreber (2011) ‘Gender, stock market participation and finan-

cial literacy.’ Working Paper Series in Economics and Finance 737, Stockholm School of

Economics, Aug

Ameriks, John, and Stephen Zeldes (2004) ‘How do household portfolio shares vary with age?’

Technical Report, TIAA-CREF Working Paper

Arrow, Kenneth J. (1987) ‘The demand for information and the distribution of income.’ Prob-

ability in the Engineering and Informational Sciences 1, 3–13

Banks, James, and Zoë Oldfield (2007) ‘Understanding pensions: Cognitive function, numerical

ability and retirement saving.’ Fiscal Studies 28(2), 143–170

Behrman, Jere R., Olivia S. Mitchell, Cindy Soo, and David Bravo (2012) ‘Financial literacy,

schooling, and wealth accumulation.’ American Economic Review 102(3), 300–304

Calvet, Laurent E., John Y. Campbell, and Paolo Sodini (2007) ‘Down or out: Assessing the

welfare costs of household investment mistakes.’ Journal of Political Economy 115(5), 707–

747

(2009) ‘Measuring the financial sophistication of households.’ American Economic Review

99(2), 393–398

Campbell, John Y., Tarun Ramadorai, and Benjamin Ranishy (2012) ‘Do stock traders

learn from experience? evidence from an emerging market.’ Available at SSRN:

http://ssrn.com/abstract=2176222 or http://dx.doi.org/10.2139/ssrn.2176222

Card, David (2001) ‘Estimating the return to schooling: Progress on some persistent econo-

metric problems.’ Econometrica 69(5), 1127–60

Carpena, Fenella, Shawn Cole, Jeremy Shapiro, and Bilal Zia (2011) ‘Unpacking the causal

chain of financial literacy.’ Policy Research Working Paper Series 5798, The World Bank,

September

28

Christelis, Dimitris (2008) ‘Item non-response in Share Wave 2.’ First Results from the Sur-

vey on Health, Aging and Retirement in Europe (2004-2007): Starting the Longitudinal

Dimension

Christelis, Dimitris, Tullio Jappelli, and Mario Padula (2010) ‘Cognitive abilities and portfolio

choice.’ European Economic Review 54(1), 18–38

Christiansen, Charlotte, Juanna S. Joensen, and Jesper Rangvid (2008) ‘Are economists more

likely to hold stocks?’ Review of Finance 12(3), 465–496

Delavande, Adeline, Susann Rohwedder, and Robert Willis (2008) ‘Preparation for retirement,

financial literacy and cognitive resources.’ Working Papers wp190, University of Michigan,

Michigan Retirement Research Center, September

Dewey, Michael E., and Martin J. Prince (2005) ‘Cognitive function.’ In Health, Aging and

Retirement in Europe: First Results from the Survey of Health, Aging and Retirement

in Europe, ed. Axel Börsch-Supan, Agar Brugiavini, Hendrik Jürges, Johan Mackenbach,

Johannes Siegrist, and Guglielmo Weber (Mannheim: Mannheim Research Institute for

the Economics of Aging (MEA)) pp. 118–125

Disney, Richard F. (2004) ‘Are contributions to public pension programmes a tax on employ-

ment?’ Economic Policy 19(39), 267–311

Feng, Lei, and Mark Seasholes (2005) ‘Do investor sophistication and trading experience elim-

inate behavioral biases in financial markets?’ Review of Finance 9, 305–351

Grinblatt, Mark, and Matti Keloharju (2001) ‘What makes investors trade?’ Journal of Finance

56(2), 589–616

Guiso, Luigi, and Tullio Jappelli (2008) ‘Financial literacy and portfolio diversification.’ Tech-

nical Report, CSEF Working Paper 212

Guiso, Luigi, Michael Haliassos, and Tullio Jappelli (2003) ‘Household stockholding in europe:

where do we stand and where do we go?’ Economic Policy 18(36), 123–170

Hackethal, Andreas, Michael Haliassos, and Tullio Jappelli (2012) ‘Financial advisors: A case

of babysitters?’ Journal of Banking & Finance 36(2), 509–524

29

Haliassos, Michael, and Carol C Bertaut (1995) ‘Why do so few hold stocks?’ Economic Journal

105(432), 1110–29

Hastings, Justine S., Brigitte C. Madrian, and William L. Skimmyhorn (2012) ‘Financial liter-

acy, financial education and economic outcomes.’ NBER Working Papers 18412, National

Bureau of Economic Research, Inc, September

Herd, Pamela, Karen Holden, and Yund Ting Su (2012) ‘The links between early-life cognition

and schooling and late-life financial knowledge.’ Journal of Consumer Affairs 46(3), 411–

435

Jappelli, Tullio, and Mario Padula (2013) ‘Investment in financial literacy and saving decisions.’

Journal of Banking and Finance. forthcoming

Kennickell, Arthur B. (1991) ‘Imputation of the 1989 Survey of Consumer Finances: Stochas-

tic relaxation and multiple imputation.’ ASA 1991 Proceedings of the Section on Survey

Research Methods pp. 1–10

Klevmarken, Anders (2005) ‘Sample design.’ In Health, ageing and retirement in Europe: First

results from the Survey of Health, Ageing and Retirement in Europe., ed. Axel Börsch-

Supan, Agar Brugiavini, Hendrik Jürges, Johan Mackenbach, Johannes Siegrist, and

Guglielmo Weber (Mannheim: Mannheim Research Institute for the Economics of Ag-

ing (MEA)) p. 352

Lusardi, Annamaria, and Olivia S. Mitchell (2007) ‘Baby boomer retirement security: The

roles of planning, financial literacy, and housing wealth.’ Journal of Monetary Economics

54(1), 205–224

Lusardi, Annamaria, and Olivia S. Mitchell (2008) ‘Planning and financial literacy: How do

women fare?’ American Economic Review 98(2), 413–417

Lusardi, Annamaria, Olivia S. Mitchell, and Vilsa Curto (2010) ‘Financial literacy among the

young.’ Journal of Consumer Affairs 44(2), 358–380

OECD (2013) ‘Financial literacy framework.’ In ‘OECD, PISA 2012 Assessment and Analytical

Framework: Mathematics, Reading, Science, Problem Solving and Financial Literacy’

(OECD publishing)

30

Stango, Victor, and Jonathan Zinman (2009) ‘Exponential growth bias and household finance.’

Journal of Finance 64(6), 2807–2849

van Rooij, Maarten, Annamaria Lusardi, and Rob Alessie (2011) ‘Financial literacy and stock

market participation.’ Journal of Financial Economics 101(2), 449–472

Vissing-Jorgensen, Annette (2002) ‘Limited asset market participation and the elasticity of

intertemporal substitution.’ Journal of Political Economy 110(4), 825–853

Willis, Robert J. (2009) ‘Disentangling cognitive function and financial literacy: Implications for

financial retirement security research.’ presented at the Conference on Financial Literacy

in Times of Turmoiland Retirement Insecurity, Brookings Institution, Washington, D.C.,

March 20, 2009

Zhu, Ning (2002) ‘The local bias of individual investors.’ Working Paper 02-30, Yale ICF

31

Table 1: Summary statistics

Mean Std. Dev N

Wave 1

Age 63.577 9.272 14,631Female 0.545 0.498 14,631Single 0.242 0.428 14,631Family size 2.204 0.985 14,631Log income 10.571 1.384 14,555Log wealth 12.141 1.726 14,631High school 0.298 0.457 14,631College 0.202 0.402 14,631Health status 3.159 1.015 14,631Replacement rate 0.742 0.221 14,631Φt 3.426 1.087 14,631Φ0 3.296 0.895 14,631

Wave 2

Age 64.335 9.514 18,332Female 0.542 0.498 18,332Single 0.235 0.424 18,332Family size 2.182 0.953 18,332Log income 10.474 1.406 18,141Log wealth 12.423 1.705 18,332High school 0.318 0.466 18,332College 0.212 0.409 18,332Health status 3.060 1.054 18,332Replacement rate 0.731 0.224 18,332Φt 3.481 1.107 18,332Φ0 3.297 0.898 18,332

Note: The table reports sample statistics for selected variables in SHARE Wave 1 (top panel) and Wave 2(bottom panel). In Wave 1 income is gross of taxes, in Wave 2 it is net of taxes. Wave 1 refers to 2003 andWave 2 to 2006.

32

Tab

le2:

Fin

anci

allite

racy

Wave

1W

ave

2

Age

−0.

017∗∗∗

−0.

015∗∗∗

−0.0

19∗∗∗

−0.0

17∗∗∗

(0.0

01)

(0.0

01)

(0.0

01)

(0.0

01)

Fem

ale

−0.

313∗∗∗

−0.

302∗∗∗

−0.

300∗∗∗

−0.2

92∗∗∗

−0.2

81∗∗∗

−0.2

77∗∗∗

(0.0

14)

(0.0

14)

(0.0

14)

(0.0

13)

(0.0

13)

(0.0

13)

Sin

gle

−0.

064∗∗∗

−0.

031

−0.

010

−0.

091∗∗∗

−0.0

70∗∗∗

−0.0

45∗∗

(0.0

20)

(0.0

20)

(0.0

20)

(0.0

18)

(0.0

18)

(0.0

19)

Fam

ily

size

−0.

030∗∗∗

−0.

037∗∗∗

−0.

027∗∗∗

−0.

037∗∗∗

−0.0

41∗∗∗

−0.0

31∗∗∗

(0.0

09)

(0.0

09)

(0.0

09)

(0.0

08)

(0.0

09)

(0.0

09)

Hig

hsc

hool

0.40

0∗∗∗

0.36

1∗∗∗

0.36

0∗∗∗

0.3

52∗∗∗

0.3

18∗∗∗

0.3

18∗∗∗

(0.0

18)

(0.0

18)

(0.0

18)

(0.0

16)

(0.0

16)

(0.0

16)

Coll

ege

0.58

6∗∗∗

0.50

9∗∗∗

0.50

9∗∗∗

0.5

30∗∗∗

0.4

64∗∗∗

0.4

65∗∗∗

(0.0

20)

(0.0

21)

(0.0

21)

(0.0

18)

(0.0

19)

(0.0

19)

Φ0

0.30

0∗∗∗

0.29

3∗∗∗

0.29

3∗∗∗

0.28

9∗∗∗

0.2

71∗∗∗

0.2

72∗∗∗

(0.0

25)

(0.0

25)

(0.0

25)

(0.0

22)

(0.0

22)

(0.0

22)

Φ0×ρ

−0.

163∗∗∗

−0.

162∗∗∗

−0.

162∗∗∗

−0.1

31∗∗∗

−0.1

16∗∗∗

−0.1

17∗∗∗

(0.0

33)

(0.0

33)

(0.0

33)

(0.0

29)

(0.0

29)

(0.0

29)

Hea

lth

stat

us

0.10

2∗∗∗

0.10

1∗∗∗

0.1

17∗∗∗

0.1

17∗∗∗

(0.0

07)

(0.0

08)

(0.0

07)

(0.0

07)

Log

inco

me

0.06

1∗∗∗

0.06

2∗∗∗

0.0

40∗∗∗

0.0

41∗∗∗

(0.0

08)

(0.0

08)

(0.0

07)

(0.0

07)

N14

,631

14,5

5514

,508

18,

332

18,1

41

18,0

55

Fu

llse

tof

age

du

mm

ies

No

No

Yes

No

No

Yes

Note

:A

llre

gres

sion

sin

clu

de

afu

llse

tof

cou

ntr

yd

um

mie

s.W

ave

1re

fers

to2003

an

dW

ave

2to

2006.

*p<

0.1,

**p<

0.05,

***p<

0.0

1.

Sta

nd

ard

erro

rsin

pare

nth

eses

.

33

Tab

le3:

Dir

ect

stock

-mar

ket

par

tici

pat

ion

Wave

1W

ave

2

Age

−0.

002∗∗∗

−0.

001∗∗

−0.0

01∗∗∗

−0.0

01∗∗

(0.0

00)

(0.0

00)

(0.0

00)

(0.0

00)

Fem

ale

−0.

007

−0.

004

−0.

004

−0.

004

−0.0

05

−0.0

03

(0.0

06)

(0.0

06)

(0.0

06)

(0.0

06)

(0.0

06)

(0.0

06)

Sin

gle

−0.

095∗∗∗

−0.

030∗∗∗

−0.

065∗∗∗

−0.

095∗∗∗

−0.0

32∗∗∗

−0.0

26∗∗∗

(0.0

09)

(0.0

09)

(0.0

09)

(0.0

08)

(0.0

08)

(0.0

08)

Fam

ily

size

−0.

006

−0.

011∗∗∗

−0.

009∗∗

−0.0

12∗∗∗

−0.0

16∗∗∗

−0.0

13∗∗∗

(0.0

04)

(0.0

04)

(0.0

04)

(0.0

04)

(0.0

04)

(0.0

04)

Hig

hsc

hool

0.04

6∗∗∗

0.01

5∗

0.02

9∗∗∗

0.0

61∗∗∗

0.0

31∗∗∗

0.0

31∗∗∗

(0.0

08)

(0.0

08)

(0.0

08)

(0.0

07)

(0.0

07)

(0.0

07)

Coll

ege

0.15

0∗∗∗

0.08

5∗∗∗

0.11

2∗∗∗

0.1

38∗∗∗

0.0

77∗∗∗

0.0

76∗∗∗

(0.0

09)

(0.0

09)

(0.0

09)

(0.0

08)

(0.0

08)

(0.0

08)

Φ0

0.06

9∗∗∗

0.05

6∗∗∗

0.06

8∗∗∗

0.06

7∗∗∗

0.0

52∗∗∗

0.0

52∗∗∗

(0.0

11)

(0.0

11)

(0.0

11)

(0.0

10)

(0.0

10)

(0.0

10)

Φ0×ρ

−0.

066∗∗∗

−0.

056∗∗∗

−0.

069∗∗∗

−0.0

65∗∗∗

−0.0

55∗∗∗

−0.0

55∗∗∗

(0.0

14)

(0.0

14)

(0.0

14)

(0.0

13)

(0.0

13)

(0.0

13)

Hea

lth

stat

us

0.01

2∗∗∗

0.01

9∗∗∗

0.0

06∗∗

0.0

06∗∗

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

03)

Log

inco

me

0.04

1∗∗∗

0.05

7∗∗∗

0.0

28∗∗∗

0.0

28∗∗∗

(0.0

04)

(0.0

04)

(0.0

03)

(0.0

03)

Log

wea

lth

0.05

3∗∗∗

0.0

60∗∗∗

0.0

60∗∗∗

(0.0

02)

(0.0

02)

(0.0

02)

N14

,631

14,5

5514

,508

18,

332

18,1

41

18,0

55

Fu

llse

tof

age

du

mm

ies

No

No

Yes

No

No

Yes

Note

:A

llre

gres

sion

sin

clu

de

afu

llse

tof

cou

ntr

yd

um

mie

s.W

ave

1re

fers

to2003

an

dW

ave

2to

2006.

*p<

0.1,

**p<

0.05,

***p<

0.0

1.